Practical Signal Analysis: Do Wavelets Make Any Difference?

1997 ◽  
Author(s):  
David E. Newland
Keyword(s):  
Signal Analysis ◽  
Simple Structure ◽  
Essential Element ◽  
Signal Decomposition ◽  
High Definition ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
Harmonic Wavelet ◽  
Short Time ◽  
Better Than

Abstract Signal decomposition by time-frequency and time-scale mapping is an essential element of most diagnostic signal analysis. Is the wavelet method of decomposition any better than the short-time Fourier transform and Wigner-Ville methods? This paper explores the effectiveness of wavelets for diagnostic signal analysis. The author has found that harmonic wavelets are particularly suitable because of their simple structure in the frequency domain, but it is still difficult to produce high-definition time-frequency maps. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition.

Ridge and Phase Identification in the Frequency Analysis of Transient Signals by Harmonic Wavelets

1999 ◽  
Vol 121 (2) ◽  
pp. 149-155 ◽  
Author(s):  
D. E. Newland
Keyword(s):  
Frequency Analysis ◽  
Phase Identification ◽  
Computational Algorithms ◽  
High Definition ◽  
Diagnostic Features ◽  
Transient Signals ◽  
Phase Gradient ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
Harmonic Wavelet

It is difficult to generate high-definition time-frequency maps for rapidly changing transient signals. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition. Features of these algorithms include the use of ridge identification and phase gradient as diagnostic features.

scholarly journals Classification of Hydroacoustic Signals Based on Harmonic Wavelets and a Deep Learning Artificial Intelligence System

2020 ◽  
Vol 10 (9) ◽  
pp. 3097
Author(s):  
Dmitry Kaplun ◽  
Alexander Voznesensky ◽  
Sergei Romanov ◽  
Valery Andreev ◽  
Denis Butusov
Keyword(s):  
Fourier Transform ◽  
Deep Learning ◽  
Feature Space ◽  
Roc Curves ◽  
Harmonic Wavelets ◽  
Intelligence System ◽  
Stationary Signals ◽  
Harmonic Wavelet ◽  
Short Time

This paper considers two approaches to hydroacoustic signal classification, taking the sounds made by whales as an example: a method based on harmonic wavelets and a technique involving deep learning neural networks. The study deals with the classification of hydroacoustic signals using coefficients of the harmonic wavelet transform (fast computation), short-time Fourier transform (spectrogram) and Fourier transform using a kNN-algorithm. Classification quality metrics (precision, recall and accuracy) are given for different signal-to-noise ratios. ROC curves were also obtained. The use of the deep neural network for classification of whales’ sounds is considered. The effectiveness of using harmonic wavelets for the classification of complex non-stationary signals is proved. A technique to reduce the feature space dimension using a ‘modulo N reduction’ method is proposed. A classification of 26 individual whales from the Whale FM Project dataset is presented. It is shown that the deep-learning-based approach provides the best result for the Whale FM Project dataset both for whale types and individuals.

The Applicated Comparation of Three Signal Analytical Methods for Ocean CSEM Signature

2013 ◽  
Vol 798-799 ◽  
pp. 561-564
Author(s):  
Ji Yu Zhou ◽  
Feng Dao Zhou
Keyword(s):  
Frequency Analysis ◽  
Oil And Gas ◽  
Time Frequency Analysis ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Analysis Technique ◽  
Oil And Gas Resources ◽  
Concentration Degree ◽  
Short Time ◽  
Better Than

Sea is rich in oil and gas resources, the marine controlled source electromagnetic method (CSEM) is a kind of method seabed oil gas geophysical technology rising in recent years. Because of the problem of CSEM about the air wave in the shallow water, the research of time-frequnecy analysis technique is used to suppress the air wave in this paper. The basic idea is: because of the CSEM signals speed are different in the air and submarine, so the time which received by the receiving points are also different through these two kinds of ways. Using the time-frequency analysis technique and theoretical calculation, we can determine which part of the signal is spread over the ocean, so as to suppress the air wave effectively. This paper lists several methods of time-frequency analysis, such as Short-time Fourier transform, W-V distribution, Wavelet transform, Hilbert Huang transform. Through the time-frequency graph,we get the conclusion that HHT is better than others in concentration degree,and W-V distribution is better than STFT.Compared with the original signal, the time-frequency graph is the best in using Smooth Puseudo W-V Distribution.I have a detailed analysis about real case in using SPWVD at last.

Wavelet Analysis of Vibration: Part 1—Theory

1994 ◽  
Vol 116 (4) ◽  
pp. 409-416 ◽  
Author(s):  
D. E. Newland
Keyword(s):  
Signal Analysis ◽  
Spectral Composition ◽  
Vibration Measurement ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
Orthogonal Wavelets ◽  
Vibration Data ◽  
Measurement And Analysis ◽  
Frequency Map ◽  
Selection Of

Wavelets provide a new tool for the analysis of vibration records. They allow the changing spectral composition of a nonstationary signal to be measured and presented in the form of a time-frequency map. The purpose of this paper, which is Part 1 of a pair, is to introduce and review the theory of orthogonal wavelets and their application to signal analysis. It includes the theory of dilation wavelets, which have been developed over a period of about ten years, and of harmonic wavelets which have been proposed recently by the author. Part II is about presenting the results on wavelet maps and gives a selection of examples. The papers will interest those who work in the field of vibration measurement and analysis and who are in positions where it is necessary to understand and interpret vibration data.

scholarly journals Applications of Fractional Lower Order Synchrosqueezing Transform Time Frequency Technology to Machine Fault Diagnosis

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Haibin Wang ◽  
Junbo Long
Keyword(s):  
Lower Order ◽  
Signal Analysis ◽  
Stable Distribution ◽  
Signal Reconstruction ◽  
Outer Race ◽  
Time Frequency ◽  
S Transform ◽  
Synchrosqueezing Transform ◽  
Better Than ◽  
Low Order

Synchrosqueezing transform (SST) is a high resolution time frequency representation technology for nonstationary signal analysis. The short time Fourier transform-based synchrosqueezing transform (FSST) and the S transform-based synchrosqueezing transform (SSST) time frequency methods are effective tools for bearing fault signal analysis. The fault signals belong to a non-Gaussian and nonstationary alpha (α) stable distribution with 1<α<2 and even the noises being also α stable distribution. The conventional FSST and SSST methods degenerate and even fail under α stable distribution noisy environment. Motivated by the fact that fractional low order STFT and fractional low order S-transform work better than the traditional STFT and S-transform methods under α stable distribution noise environment, we propose in this paper the fractional lower order FSST (FLOFSST) and the fractional lower order SSST (FLOSSST). In addition, we derive the corresponding inverse FLOSST and inverse FLOSSST. The simulation results show that both FLOFSST and FLOSSST perform better than the conventional FSSST and SSST under α stable distribution noise in instantaneous frequency estimation and signal reconstruction. Finally, FLOFSST and FLOSSST are applied to analyze the time frequency distribution of the outer race fault signal. Our results show that FLOFSST and FLOSSST extract the fault features well under symmetric stable (SαS) distribution noise.

scholarly journals Sampled and discretized of short-time Fourier transform and non-negative matrix factorization: the single-channel source separation case

2020 ◽  
Vol 9 (1) ◽  
pp. 41-48
Author(s):  
Jans Hendry ◽  
Isnan Nur Rifai ◽  
Yoga Mileniandi
Keyword(s):  
Fourier Transform ◽  
Matrix Factorization ◽  
Single Channel ◽  
Source Separation ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
Short Time ◽  
Better Than ◽  
Non Negative Matrix Factorization

The Short-time Fourier transform (STFT) is a popular time-frequency representation in many source separation problems. In this work, the sampled and discretized version of Discrete Gabor Transform (DGT) is proposed to replace STFT within the single-channel source separation problem of the Non-negative Matrix Factorization (NMF) framework. The result shows that NMF-DGT is better than NMF-STFT according to Signal-to-Interference Ratio (SIR), Signal-to-Artifact Ratio (SAR), and Signal-to-Distortion Ratio (SDR). In the supervised scheme, NMF-DGT has a SIR of 18.60 dB compared to 16.24 dB in NMF-STFT, SAR of 13.77 dB to 13.69 dB, and SDR of 12.45 dB to 11.16 dB. In the unsupervised scheme, NMF-DGT has a SIR of 0.40 dB compared to 0.27 dB by NMF-STFT, SAR of -10.21 dB to -10.36 dB, and SDR of -15.01 dB to -15.23 dB.

Application of Harmonic Wavelet Analysis to Rubbing Vibration Signals for Rotating Machinery Fault Diagnosis

2013 ◽  
Vol 321-324 ◽  
pp. 1245-1248
Author(s):  
Xiang Wang ◽  
Yuan Zheng
Keyword(s):  
Wavelet Transform ◽  
Signal Analysis ◽  
Rotating Machinery ◽  
The Other ◽  
Vibration Signals ◽  
Time Frequency ◽  
Vibration Data ◽  
Turbo Generator ◽  
Harmonic Wavelet ◽  
Machinery Fault Diagnosis

Harmonic wavelet transform (HWT)and harmonic wavelet time-frequency profile plot (TFPP) is introduced firstly in practice to identify weak singularity in a signal with noise clearly. With TFPP method, emulational signal and vibration data of the rubbing of the large practical turbo-generator units are analyzed successfully, which prove that the method is effectively extract the rubbing signal feature which is can not gained by the other signal analysis methods, and the rubbing of the turbo-generator units is identified effectively.

Harmonic wavelet analysis

1993 ◽  
Vol 443 (1917) ◽  
pp. 203-225 ◽  
Keyword(s):  
Fourier Coefficients ◽  
Simple Structure ◽  
Functional Form ◽  
Orthogonal Transformation ◽  
Octave Band ◽  
Harmonic Wavelets ◽  
Inverse Transform ◽  
Harmonic Wavelet ◽  
Dilation Equations ◽  
Discrete Transform

A new harmonic wavelet is suggested. Unlike wavelets generated by discrete dilation equations, whose shape cannot be expressed in functional form, harmonic wavelets have the simple structure ω(x) = {exp(i4π x ) - exp(i2π x )}/i2π x . This function ω(x) is concentrated locally around x = 0, and is orthogonal to its own unit translations and octave dilations. Its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain (rather than in the x domain). An efficient implementation of a discrete transform using this wavelet is based on the fast Fourier transform (FFT). Fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the FFT. The same process works backwards for the inverse transform.

Linear Multi-Degree-of-Freedom System Stochastic Response by Using the Harmonic Wavelet Transform

2003 ◽  
Vol 70 (5) ◽  
pp. 724-731 ◽  
Author(s):  
P. Tratskas ◽  
P. D. Spanos
Keyword(s):  
Wavelet Transform ◽  
Linear System ◽  
Spectral Characteristics ◽  
Degree Of Freedom ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
The Family ◽  
Harmonic Wavelet ◽  
The Time Domain ◽  
System Frequency

The wavelet transform is used to capture localized features in either the time domain or the frequency domain of the response of a multi-degree-of-freedom linear system subject to a nonstationary stochastic excitation. The family of the harmonic wavelets is used due to the convenient spectral characteristics of its basis functions. A wavelet-based system representation is derived by converting the system frequency response matrix into a time-frequency wavelet “tensor.” Excitation-response relationships are obtained for the wavelet-based representation which involve linear system theory, spectral representation of the excitation and of the response vectors, and the wavelet transfer tensor of the system. Numerical results demonstrate the usefulness of the developed analytical procedure.

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